Combine half the salmon and all the cream cheese in a blender or food processor and puree. Spread a thin layer of the cream cheese mixture on each slice of bread. Spoon the remaining spread into a piping bag fitted with a star tip, if desired.

Top each slice of bread with remaining smoked salmon. Using a 3-inch oval cutter cut out about 16 sandwiches. Pipe rosettes of the cream cheese mixture onto each of the sandwiches, and then press parsley around the edge of each oval of bread.

Arrange the sandwiches on 4 plates. Garnish the sandwiches with cucumber and salmon roe and serve.